Course Description
Asymptotic inference for maximum likelihood estimators, M- estimators, U-statistics, and nonparametric and semiparametric models. Consistency, asymptotic normality, and asymptotic efficiency are considered. Both independent and dependent data cases are included. Emphasis is given to results needed to develop and evaluate biostatistical methods rather than rigorous mathematical proofs.
Athena Title
Asymptotic Biostatistical Infe
Prerequisite
BIOS 8310
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
The aim of this course and its prerequisite (BIOS 8310) is to train students in the theoretical foundations required to evaluate the mathematical and statistical properties of new and innovative biostatistical methods. Students completing this course should be able to: 1. Contrast different classes of estimators, including maximum likelihood, M-estimators, and U-statistics; 2. Construct mathematical proofs for the consistency and asymptotic normality of parameter estimators; 3. Evaluate the small- and large-sample properties of resampling methods, including jackknife and bootstrap; 4. Use empirical process theory to evaluate the properties of nonparametric and semiparametric estimators; 5. Explain stochastic process models, including Poisson processes, Markov chains, and birth and death processes; 6. Explain conditions for Martingale laws of large numbers and central limit theorems.
Topical Outline
1. Maximum Likelihood Estimation 2. EM Algorithm 3. M-Estimators 4. U-Statistics 5. Robust Inference 6. Empirical Process Theory 7. Nonparametric and semiparametric Estimators 8. Resampling Methods 9. Stochastic Processes 10. Martingales 11. Asymptotic Inference for Longitudinal Data
Syllabus
Public CV